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Highway dimension, shortest paths, and provably efficient algorithms
 IN ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA’10) JANUARY 1719, 2010
, 2010
"... Computing driving directions has motivated many shortest path heuristics that answer queries on continental scale networks, with tens of millions of intersections, literally instantly, and with very low storage overhead. In this paper we complement the experimental evidence with the first rigorous p ..."
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Cited by 40 (3 self)
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proofs of efficiency for many of the heuristics suggested over the past decade. We introduce the notion of highway dimension and show how low highway dimension gives a unified explanation for several seemingly different algorithms.
Asymptotically efficient latticebased digital signatures
 IN FIFTH THEORY OF CRYPTOGRAPHY CONFERENCE (TCC
, 2008
"... We give a direct construction of digital signatures based on the complexity of approximating the shortest vector in ideal (e.g., cyclic) lattices. The construction is provably secure based on the worstcase hardness of approximating the shortest vector in such lattices within a polynomial factor, an ..."
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Cited by 28 (9 self)
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, and it is also asymptotically efficient: the time complexity of the signing and verification algorithms, as well as key and signature size is almost linear (up to polylogarithmic factors) in the dimension n of the underlying lattice. Since no subexponential (in n) time algorithm is known to solve lattice
Maximum Thick Paths in Static and Dynamic Environments
, 2008
"... We consider the problem of finding a maximum number of disjoint paths for unit disks moving amidst static or dynamic obstacles. For the static case we give efficient exact algorithms, based on adapting the “continuous uppermost path” paradigm. As a byproduct, we establish a continuous analogue of M ..."
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Cited by 6 (5 self)
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is not possible (unless P=NP), a careful choice of time discetization and a nonuniform grid of “waypoints ” allows us to give provable approximation guarantees on the quality of the solution produced by the algorithm. Our algorithm extends to higher dimensions and to finding paths for translational motion
Further mathematical properties of Cayley digraphs applied to hexagonal and honeycomb meshes
"... In this paper, we extend known relationships between Cayley (di)graphs and their subgraphs and coset graphs with respect to subgroups to obtain a number of general results on homomorphism between them. Intuitively, our results correspond to synthesizing alternative, more economical, interconnectio ..."
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Cited by 6 (3 self)
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, interconnection networks by reducing the number of dimensions and/or link density of existing networks via mapping and pruning. We discuss applications of these results to wellknown and useful interconnection networks such as hexagonal and honeycomb meshes, including the derivation of provably correct shortestpath
Navigating in unfamiliar geometric terrain (preliminary version
 In Proceedings of the Twenty Third Annual ACM Symposium on Theory of Computing
, 1991
"... Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rathe ..."
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Cited by 1 (0 self)
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; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from.s to t to the length of the shortest path between s and t in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we
Depth of field and cautiousgreedy routing in social networks
 In Proceedings of the 18th International Symposium on Algorithms and Computation
, 2007
"... Social networks support efficient decentralized search: people can collectively construct short paths to a specified target in the network. Rankbased friendship—where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is—is ..."
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Cited by 5 (2 self)
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Social networks support efficient decentralized search: people can collectively construct short paths to a specified target in the network. Rankbased friendship—where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR
"... 2010 to my wife, Joyce, and my family... Résumé ..."
Lattice Based Cryptography
, 2003
"... Cryptographic applications of lattices include both cyptanalysis and the design of (provably secure) cryptographic functions. Cryptanalysis applications are usually based on lattice reduction techniques. The name “lattice based cryptography ” typically refers to the second kind of applications: usin ..."
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of the knapsack problem are at least as hard to break on the average as the worst case instance of certain lattice problems, e.g., solving the Shortest Vector Problem (SVP) approximately within polynomial factors. Specifically, assuming that there is no efficient algorithm to approximate SVP within a factor g = n
Supervised by
, 2007
"... I would like to thank my parents for always believing in me. I would also like to thank my supervisors Richard Lindner and Johannes Buchmann for their useful comments and suggestions on how to improve the queality of the thesis. Not on last place I would like to thank Vadim Lyubashevsky and Luis Car ..."
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I would like to thank my parents for always believing in me. I would also like to thank my supervisors Richard Lindner and Johannes Buchmann for their useful comments and suggestions on how to improve the queality of the thesis. Not on last place I would like to thank Vadim Lyubashevsky and Luis Carlos Coronado Garcia for their kindness and readiness to answer my questions. Warranty I hereby warrant that the content of this thesis is the direct result of my own work and that any use made in it of published or unpublished material is fully and correctly referenced. I also warrant that the presented work has
Results 1  10
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